WP API Response does not show my registered metadata

For posts (Posts, Pages and custom post types), the very first parameter for register_meta() is always post and to set a custom post type, use the object_subtype argument in the third parameter like so:

$meta_args = array(
    'object_subtype' => 'splash_location', // the post type
    'type'           => 'string',
    'description'    => 'A meta key associated with a string meta value.',
    'single'         => true,
    'show_in_rest'   => true,
);
register_meta( 'post', 'splash_location_title', $meta_args );

Or you could instead use register_post_meta() which accepts the post type as the first parameter:

$meta_args = array(
    'type'         => 'string',
    'description'  => 'A meta key associated with a string meta value.',
    'single'       => true,
    'show_in_rest' => true,
);
register_post_meta( 'splash_location', 'splash_location_title', $meta_args );

So in your existing code, you’d simply replace the register_meta with register_post_meta.. 🙂